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TECHNICAL PAPERS: Conduction Heat Transfer

Inverse Determination of Temperature-Dependent Thermal Conductivity Using Steady Surface Data on Arbitrary Objects

[+] Author and Article Information
T. J. Martin

Turbine System & Optimization, M/S 201-20, Pratt & Whitney Aircraft Company, 400 Main Street, East Hartford, CT 06108e-mail: martinj@pweh.com

G. S. Dulikravich

Department of Mechanical and Aerospace Engineering, Box 19018, The University of Texas at Arlington, Arlington, TX 76019 e-mail: dulikra@mae.uta.edu

J. Heat Transfer 122(3), 450-459 (Feb 14, 2000) (10 pages) doi:10.1115/1.1287726 History: Received April 12, 1999; Revised February 14, 2000
Copyright © 2000 by ASME
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References

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Martin, T. J., and Dulikravich, G. S., 1997, “Non-Iterative Inverse Determination of Temperature-Dependent Heat Conductivities,” Symposium on Inverse Design Problems in Heat Transfer and Fluid Flow, Vol. 2, G. S. Dulikravich, and K. A. Woodbury, eds., ASME, New York, pp. 141–150.
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Figures

Grahic Jump Location
Variation of the thermal conductivity versus temperature for various amounts of input error in temperature (a) σ=0.0°C, (b) σ=0.1 °C, (c) σ=1.0°C, and (d) σ=5.0°C. The inverse boundary element method results are compared to the actual linear conductivity versus temperature function, where β=0.05°C−1,T0=0.0°C, and k0=1.0 W m−1°C.
Grahic Jump Location
Predicted temperature-dependence of thermal conductivity when errors were added to the heat fluxes compared to the actual linear variation of k(T)
Grahic Jump Location
Variation of the thermal conductivity versus temperature for various levels of input error in temperature, (a): σ=0.0°C, and (b): σ=0.5°C. The boundary element method results are compared to the actual arctangent conductivity versus temperature function when δ=1.0°C−1.
Grahic Jump Location
Variation of the thermal conductivity versus temperature for various levels of input error in temperature, (a): σ=1.0°C, and (b): σ=5.0°C. The inverse boundary element method results are compared to the actual arctangent conductivity versus temperature function when δ=1.0°C−1.
Grahic Jump Location
Variation of thermal conductivity versus temperature predicted with the beta-spline basis functions. The inverse boundary element method results are compared to the actual arctangent conductivity versus temperature function when δ=1.0°C−1.
Grahic Jump Location
Variation of thermal conductivity versus temperature predicted with the integrated beta-spline basis functions. The inverse boundary element method results are compared to the actual arctangent conductivity versus temperature function when δ=1.0°C−1.
Grahic Jump Location
Inverse determination of the thermal conductivity of copper in the cryogenic range. The best inverse results are shown with various levels of input error:(a) σ=0.0 K, (b) σ=0.1 K, and (c) σ=1.0 K.
Grahic Jump Location
Temperature contours predicted by nonlinear boundary element method within an arbitrarily shape specimen that was internally heated and made of copper (b)
Grahic Jump Location
Inverse prediction of thermal conductivity variation of an arbitrarily shaped specimen made of copper

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